Question

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. A solid oblique pyramid has an equilateral triangle base with an edge length of s units. Which expression represents the height of the triangular base of the pyramid? Five-halves StartRoot 2 EndRootunits Five-halves StartRoot 3 EndRootunits 5 StartRoot 2 EndRootunits 5 StartRoot 3 EndRootunits

Answer 1

the height of the triangular base of the pyramid is Five-halves StartRoot 3 EndRootunits = (5/2)√3 units

Explanation:

An image of the sketch of the equilateral triangle is attached to this solution.

The height of the equilateral triangle base of the pyramid divides the equilateral triangle into two equal parts as shown in the image. And it also dimensions the bottom side into two equal parts of 5/2 units each.

Let this height be called h

Using Pythagoras theorem,

5² = h² + (5/2)²

s² = h² + (s

5²/4)

h² = 5² - (5²/4)

h² = 75/4

h = √(75/4)

h = (5/2)√3 units

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